n!/m! == Pochhammer[m + 1, n - m]

Cell[BoxData[RowBox[List[FractionBox[RowBox[List["n", "!"]], RowBox[List["m", "!"]]], "\[Equal]", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["m", "+", "1"]], ",", RowBox[List["n", "-", "m"]]]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mrow> <mi> m </mi> <mo> ! </mo> </mrow> </mfrac> <mo> &#10869; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> m </mi> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;m&quot;, &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;m&quot;]]], Pochhammer] </annotation> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <factorial /> <ci> n </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List["n_", "!"]], RowBox[List["m_", "!"]]], "]"]], "\[RuleDelayed]", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["m", "+", "1"]], ",", RowBox[List["n", "-", "m"]]]], "]"]]]]]]

2001-10-29